Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 255

4

M=66

2

0

-2

-4

0 50 100 150 200 250

Number of samples

1.5

1

0.5

0

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

FIGURE 7.23

The clean signal and spectrum with noise removed.

Program 7.7. MATLAB program for the application of noise filtering.
close all; clear all
fs ¼ 8000; % Sampling rate

T ¼ 1/fs; % Sampling period

v ¼ sqrt(0.1)*randn(1,250); % Generate Gaussian random noise

n ¼ 0:1:249; % Indexes

x ¼ sqrt(2)*sin(2*pi*500*n*T) þ v; % Generate 500-Hz plus noise

subplot(2,1,1);plot(n,x);
xlabel( ' Number of samples ' );ylabel( ' Sample value ' );grid;
N ¼ length(x);
f ¼ [0:N/2]*fs/N;
Axk ¼ 2*abs(fft(x))/N;Axk(1) ¼ Axk(1)/2;

% Calculate single side spectrum for x(n)

subplot(2,1,2); plot(f,Axk(1:N/2 þ 1));
xlabel( ' Frequency (Hz) ' ); ylabel( ' Amplitude

j X(f) j ' );grid;

figure
Wnc ¼ 2*pi*900/fs;

% Determine the normalized digital cutoff

frequency
B ¼ firwd(133,1,Wnc,0,4); % Design FIR filter

y ¼ filter(B,1,x); % Perform digital filtering

Ayk ¼ 2*abs(fft(y))/N;Ayk(1) ¼ Ayk(1)/2; % Single-side spectrum of the filtered data

subplot(2,1,1); plot(n,y);